An estimation of effective thermal conductivity of a fibrous dual-scale porous medium during unsaturated flow

The effective thermal conductivity in the volume-averaged temperature equation for the dual-scale porous media is estimated numerically. A finite-element simulation of a steady Newtonian flow in the unit cell of an idealized dual-scale porous medium is carried out and the relevant component of the effective thermal conductivity tensor is estimated from the resultant temperature and velocity fields. It is discovered that the conductivity is a strong function of Péclet number as well as inter-tow spacing, but is insensitive to the rate of tow wetting or the heat-flux from tows. We also conclude that the conductivity remains unchanged in the saturated as well as unsaturated flow regimes in dual-scale porous media.